New domain decomposition algorithm for convection-dominated diffusion equations with the Samarskii scheme and the Jacobi explicit scheme

New domain decomposition algorithm for convection-dominated diffusion equations with the Samarskii scheme and the Jacobi explicit scheme | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article New domain decomposition algorithm for convection-dominated diffusion equations with the Samarskii scheme and the Jacobi explicit scheme Guanyu Xue, Yulong Gao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4556853/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A new algorithm for convection-dominated diffusion equations is proposed. Based on the domain decomposition method (DDM), the algorithm integrates the Samarskii scheme and the Jacobi explicit scheme with explicit/implicit coupling to provide parallelism. The domain decomposition method decomposes a large global problem into multiple sub-problems which can be solved on multiple processors in parallel. The parallel algorithm without needing numerical correction can obtain accuracy of Samarskii scheme while maintaining unconditional stability, which marks a step forward compared to the previous DDM. Both theoretical analysis and numerical examples show the accuracy and efficiency of the new algorithm. AMS Subject Classification: 65M06; 65M12; 65M55; 65Y05 Convection-dominated diffusion equations Domain decomposition Samarskii scheme Jacobi explicit scheme Unconditional stability Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4556853","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":319646059,"identity":"dcda7cf0-6255-447e-b785-914649da37a7","order_by":0,"name":"Guanyu Xue","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYFAD9saGAwkVEnLyxGvhOXzwwIMzFsaGDURrkUhLPviwrSKR4QABhQY3kg+/5qm5k7jhQI7BgcR5EgmMDcwPH93Ao0VyRlqaNc+xZ0AtZ4BatknksTOwGRvn4NHCL5FjZszDdjhxw8EesJZixgYeNml8Wtgk8r8Z8/wDajnMA9QyRyKx4QABLUBbmB/ztgG1HGNLOJDYQIQWyZ5nZoxz+w4bzzzDfOBAwjEJY8NmAn4xOJ78+MObb4dl++4/bP74o6ZOTp69+eFjfFrA3gESjg1wPjN+5WAlH4CEPWF1o2AUjIJRMGIBAL7VV1tzwCCjAAAAAElFTkSuQmCC","orcid":"","institution":"Yantai University","correspondingAuthor":true,"prefix":"","firstName":"Guanyu","middleName":"","lastName":"Xue","suffix":""},{"id":319646060,"identity":"69df1663-922f-4945-b207-7b0f2a833804","order_by":1,"name":"Yulong Gao","email":"","orcid":"","institution":"Hangzhou Normal University","correspondingAuthor":false,"prefix":"","firstName":"Yulong","middleName":"","lastName":"Gao","suffix":""}],"badges":[],"createdAt":"2024-06-10 08:52:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4556853/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4556853/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63947362,"identity":"81883cb1-fe1c-429c-a2b7-a5432d3e75f5","added_by":"auto","created_at":"2024-09-04 06:16:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":619509,"visible":true,"origin":"","legend":"","description":"","filename":"SamarskiiandJacobischeme.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4556853/v1_covered_26d480c2-d787-418e-a9b6-d9133e598eb2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"New domain decomposition algorithm for convection-dominated diffusion equations with the Samarskii scheme and the Jacobi explicit scheme","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Convection-dominated diffusion equations, Domain decomposition, Samarskii scheme, Jacobi explicit scheme, Unconditional stability","lastPublishedDoi":"10.21203/rs.3.rs-4556853/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4556853/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA new algorithm for convection-dominated diffusion equations is proposed. 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